Angle-dependent spin wave spectra of permalloy ring arrays

We investigated the angle-dependent spin wave spectra of permalloy ring arrays with the fixed outer diameter and various inner diameters by ferromagnetic resonance spectroscopy and micromagnetic simulation. When the field is obliquely applied to the ring, local resonance mode can be observed in different parts of the rings. And the resonance mode will change to perpendicular spin standing waves if the magnetic field is applied along the perpendicular direction. The simulation results demonstrated this evolution and implied more resonance modes that maybe exist. And the mathematical fitting results based on the Kittel equation further proved the existence of local resonance mode.